Special Session Talk: Computing equilibria in large games we play

Abstract

Describing a game using the standard (table) representation requires information
exponential in the number of players. This description size becomes impractical
for modeling large games with thousands or millions of players and is also very
wasteful since the information required to populate the game-table might be
unknown, hard to determine, or enjoy high redundancy which would allow for a
much more succinct representation. Indeed, to model large games, succinct
representations, like graphical games, have been suggested which save in
description complexity by specifying the graph of player-interactions. However,
computing Nash equilibria in such games has been shown to be an intractable
problem by Daskalakis, Goldberg and Papadimitriou, and whether approximate Nash
equilibria can be computed for graphical games remains a major open problem. We
consider instead a different class of succinct games, that of anonymous games,
in which the payoff of each player is a symmetric function of the actions of the
other players; that is, every player is oblivious of the identities of the other
players. We argue that many large games of practical interest, such as
congestion games, several auction settings, and social phenomena, are anonymous
and we provide a polynomial time approximation scheme for computing Nash
equilibria in anonymous games.